version 1.0 ABC Functional Skills Certificate Functional Mathematics 9305 Pilot Specification 2008 Level 2 SPECIMEN ASSESSMENT MATERIALS

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1 version 1.0 ABC Functional Skills Certificate Functional Mathematics 9305 Pilot Specification 2008 Level 2 SPECIMEN ASSESSMENT MATERIALS

2 Further copies of this booklet are available from: The GCSE Mathematics Department, AQA, Devas Street, Manchester, M15 6EX Telephone: Fax: Copyright 2007 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number )and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell, Director General.

3 AQA Specimen Assessment Materials, 2008 Level 2 - Functional Skills Certificate Contents Unit 1 Functional Mathematics Paper 1 Competency Specimen Paper 5 Paper 1 Competency Mark Scheme 15 Paper 2 Functionality Specimen Paper 19 Paper 2 Functionality Mark Scheme 31 Pre Release Data Sheet (Exam version) 39 Page 3

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5 Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education MATHEMATICS (PILOT) 93001/1 Unit 1 Functional Mathematics Paper 1 Competency Test Non-Calculator abc Specimen Paper (Curriculum Pathways Pilot) 2008 For this paper: You must not use a calculator Time allowed: 40 minutes Instructions Use black ink or ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. Answer the questions in the spaces provided. Do all rough work in this book. For Examiner s Use Pages Mark TOTAL Examiner s Initials Information The maximum mark for this paper is 30. The marks for questions are shown in brackets. Page /1

6 2 LEAVE MARGIN BLANK Answer all questions in the spaces provided. 1 What is to the nearest whole number? Answer... 2 Write these temperatures in order from coldest to warmest. 13 C 13 C 31 C 31 C Answer Write as a percentage. Answer... % 4 Ben has 72 pence. What is the smallest number of coins that he could have? Answer... 5 Luke is paid 4.50 per hour. He works for 8 hours. How much is he paid? Answer... 6 A parcel weighs 0.45 kilograms. What is its weight in grams? Answer... grams TS/Mar07/FMCTB2 Page 6

7 3 LEAVE MARGIN BLANK 7 You are given that 1 foot = 30 cm How many centimetres are there in 3 feet? 1 2 Answer... cm Jack uses the formula C = W + 2 to work out the charge for cleaning windows. W is the number of windows and C is the charge in pounds. How much does Jack charge for cleaning 8 windows? Answer... 9 Circle the fraction that is equivalent to 60% The table shows the number of hours which Farrah works on Saturday and Sunday. Day Saturday Sunday 1 2 Hours How many hours does she work altogether? Answer... hours TS/Mar07/FMCTB2 Page 7 Turn over 10

8 4 LEAVE MARGIN BLANK 11 The graph gives information about the sizes of households in Great Britain in Percentage of households Number of people in a household Write down the percentage of households with 4 people. Answer... % 12 A fair dice is thrown. What is the probability of getting a number greater than 4?. Answer The diagram shows a cuboid. 2 cm Not drawn accurately 3 cm 5 cm Work out its volume. Answer... cm 3 TS/Mar07/FMCTB2 Page 8

9 5 LEAVE MARGIN BLANK 14 Use the conversion graph to work out the number of kilometres that equal 80 miles miles kilometres Answer... km 15 What is two-thirds of 150? Answer What number is exactly halfway between 5 and 3? Answer... TS/Mar07/FMCTB2 Page 9 Turn over 6

10 6 LEAVE MARGIN BLANK 17 The probability that it will rain tomorrow is 0.7 What is the probability that it will not rain tomorrow? Answer A recipe for 8 people includes 1 kg of potatoes 25 g of plain flour 400 g of cabbage 240 g of mince. How many grams of cabbage are needed for 10 people? Answer... g 19 Ten numbers have a mean of 40 What is the total of the ten numbers? Answer On a scale drawing the length of a room is 5 centimetres. The scale is 1 : 200 Scale 1 : cm What is the actual length of the room? Give your answer in metres. Answer... metres TS/Mar07/FMCTB2 Page 10

11 7 LEAVE MARGIN BLANK 21 The diagram shows a scale for litres and pints. 0 1 litres pints Estimate the number of millilitres in half a pint. Give your answer to the nearest 10 millilitres. Answer... millilitres 22 Work out 5% of Answer Use the exchange rate 1 = 0.65 to convert 15 to pounds. Answer Carpet tiles are squares of side 50 centimetres. 50 cm 50 cm How many carpet tiles are required to cover a square floor of side one metre? Answer... TS/Mar07/FMCTB2 Page 11 Turn over 8

12 8 LEAVE MARGIN BLANK miles per hour and 64 kilometres per hour are the same speed. Convert 10 miles per hour to kilometres per hour. Answer... km/h 26 The diagram shows a gauge for a petrol tank. The tank holds 12 gallons when full. Full Empty Work out the number of gallons of petrol left in the tank. Answer... gallons 27 Work out Answer... TS/Mar07/FMCTB2 Page 12

13 9 LEAVE MARGIN BLANK 28 This cuboid has a continuous line drawn on it across four faces. It is a straight line on all four faces. Which of these diagrams shows the face seen from the direction of the arrow? A B C D E Answer The area of a triangle = b h 2 h The area of a triangle = 30 cm 2. The height, h = 5 cm. b Find the value of b. Answer... cm TS/Mar07/FMCTB2 Page 13 Turn over 5

14 10 LEAVE MARGIN BLANK 30 The table shows the results of a survey of where 200 people went on holiday. Country Number of people Spain 110 Scotland 50 USA 40 What percentage of people in the survey went to Scotland?.... Answer... % END OF QUESTIONS 1 TS/Mar07/FMCTB2 Page 14

15 abc General Certificate of Secondary Education Mathematics 9307 (Including Functional Mathematics) Specimen Mark Scheme Paper 1 Competency Mark Scheme 2008 examination - June series Page 15

16 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 2007 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell Director General Page 16

17 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Paper 1 Competencey Question Answer Mark Comment 1 36 B1 2 31, 13, 13, 31 B1 Ignore C 3 80 B1 4 3 B1 Accept 50 (p), 20 (p), 2 (p) 5 36 B B B1 8 6 B1 Do not accept B1 identified B1 oe Accept 11.25, 11.15, 11:15, B1 Accept 14 to 16 inclusive 12 2 B1 oe ( ) B B B B B or 30% B B B B1 Accept 270, 290, B1 Page 17

18 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Question Answer Mark Comment B B B B B1 28 E B B B1 Page 18

19 Surname Other Names For Examiner s Use Centre Number Candidate Number Candidate Signature General Certificate of Secondary Education MATHEMATICS (PILOT) 93001/2 Unit 1 Functional Mathematics Paper 2 Functionality Test Calculator allowed abc Specimen Paper (Curriculum Pathways Pilot) 2008 For this paper: a calculator mathematical instruments Time allowed: 1 hour 15 minutes Instructions Use black ink or ball-point pen. Draw diagrams in pencil. Fill in the boxes at the top of this page. Answer all questions. Answer the questions in the spaces provided. Use a calculator where appropriate. Do all rough work in this book. If your calculator does not have a π button, take the value of π to be 3.14 unless another value is given in the question. For Examiner s Use Question Mark TOTAL Examiner s Initials Information The maximum mark for this paper is 60. The marks for questions are shown in brackets. You may ask for more answer paper, graph paper and tracing paper. This must be tagged securely to this answer book. Advise In all calculations, show clearly how you work out your answer. Page /2

20 2 LEAVE MARGIN BLANK Answer all questions in the spaces provided. 1 Holiday Jobs You will need to use the Data sheet for Holiday Jobs to answer this question. (a) Ed is 13 years old. What is the maximum number of hours that he can work in one week? Answer... hours (b) Maria is 15 years old. The table shows the hours she works from Monday to Thursday. She does not work on Saturday or Sunday. Day Monday Tuesday Wednesday Thursday Friday Hours What is the greatest number of hours she can work on Friday? Answer... hours (2 marks) (c) Jenny is 17 years old. She does not work on Friday or Saturday. Her job pays the minimum wage. What is the most she can earn in a week? Answer... (3 marks) TS/Mar07/FMFTB2 Page 20

21 3 LEAVE MARGIN BLANK (d) Adnan is 14 years old. The table shows the hours he has worked on the first four days of the week. Day Monday Tuesday Wednesday Thursday Friday Hours Saturday Sunday He wants to work the maximum number of hours in the week that he can. Complete the table to show the number of hours he could work on Friday, Saturday and Sunday.... (2 marks) (e) Stacey and Ray both have a weekend holiday job. They work on Saturdays and Sundays for the maximum time allowed. Stacey is 14 years old and is paid 2.50 per hour. Ray is 16 years old and is paid the minimum wage. Stacey works for 6 weeks and Ray works for 5 weeks. Who earns the most? You must show your working Answer... (3 marks) (f) Tony is 19 years old. He works 21 hours altogether from Monday to Friday. He works 4 hours on Saturday. His pay is 4.50 per hour for Monday to Friday. On Saturday he is paid an extra 50% per hour. How much does he earn for the whole week? TS/Mar07/FMFTB2 Answer... Page 21 (4 marks) Turn over 15

22 4 LEAVE MARGIN BLANK 2 Body-Mass Index You will need to use the Data sheet for Body-Mass Index to answer this question. (a) Nicola is classified as overweight. What is the range of her BMI? Answer... to... (b) Bronwen has a BMI of 22. How is she classified? Tick the correct box. Underweight Healthy Overweight Obese (c) Jack has a body mass of 60 kg and he is 1.55 m tall. Use the graph to find his BMI. Answer... (d) (i) Katerina has a body mass of 83 kg and is 1.75 m tall. Use the formula to calculate her BMI Answer... (2 marks) (ii) How is Katerina classified? Tick the correct box. Underweight Healthy Overweight Obese TS/Mar07/FMFTB2 Page 22

23 5 LEAVE MARGIN BLANK (e) Pierre is 1.90 m tall. He is classified as healthy. Use the graph to estimate his minimum and maximum possible body mass. Answer Minimum... kg Maximum... kg (2 marks) (f) William is 1.95 m tall and has a body mass of 62 kg. He is classified as underweight. He wants to be classified as healthy on the BMI graph. How much body mass does he need to gain? Give your answer to the nearest kilogram Answer... kg (2 marks) (g) (i) Michael has a BMI of 23 and he is 1.80 m tall. Work out his body mass Answer... kg (3 marks) (ii) Paulo has the same body mass as Michael but he is taller. How does this affect his BMI? You must explain your answer (2 marks) TS/Mar07/FMFTB2 Page 23 Turn over 15

24 6 LEAVE MARGIN BLANK 3 Booklets You can make a four-page booklet by folding a single sheet of paper in two as shown. page 4 page 1 page 3 page Front and back pages Inside pages You can make an 8-page booklet by folding two sheets of paper and placing one inside the other as shown. page 7 page 7 page 1 page 1 page page 3 3 page 5 page 5 (a) How many sheets of paper do you need to make a 20-page booklet? Answer... (b) What are the two page numbers at the centre of a 40-page booklet?... Answer... and... (c) Explain why it is not possible to make a booklet with an odd number of pages TS/Mar07/FMFTB2 Page 24

25 7 LEAVE MARGIN BLANK (d) Here is the page layout for an 8-page booklet. Front and back pages Inside front and back pages Write the page numbers on the diagrams. Centre pages (3 marks) (e) Here is a single sheet for a 16-page booklet. One page is numbered. 4 Write the page number on the other page. (f) Here is a single sheet from a booklet How many pages does this booklet have altogether? Answer... (2 marks) TS/Mar07/FMFTB2 Page 25 Turn over 9

26 8 LEAVE MARGIN BLANK 4 Weather You will need to use the Data sheet for Weather to answer this question. (a) Compare the wind speeds forecast for Leeds and Paris on Saturday (b) How many more sunny days are forecast in Paris than in Leeds? Answer... (c) To go ballooning The wind speed must be less than 10 mph There must be no cloud Visibility must be good Pierre wants to go ballooning in Paris on Tuesday. According to the forecast, this will not be possible. Explain why (d) (i) Which day shows the highest day time temperature in Leeds? Answer... (ii) Which day shows the lowest night time temperature in Leeds? Answer... TS/Mar07/FMFTB2 Page 26

27 9 LEAVE MARGIN BLANK (e) To work out the daily variation in temperature Subtract the minimum night time temperature from the maximum day time temperature on the same day. (i) Work out the daily variation in temperature forecast for Saturday in Leeds.... Answer... degrees (ii) On which day and in which city is the daily variation in temperature the smallest?... Answer Day... City... (iii) According to the forecast, which city will have the largest average daily variation in temperature? You must show your working Answer... (4 marks) TS/Mar07/FMFTB2 Page 27 Turn over 11

28 10 LEAVE MARGIN BLANK 5 Household items The bar chart compares the percentage of households with different items in and in Telephone Microwave CD Player Mobile phone Home computer Tumble dryer Internet connection Dishwasher Households (%) (a) What percentage of households had a tumble dryer in ? Answer... % (b) Identify each of these items from the descriptions. (i) The percentage of households with this item in was nearly 80%. Answer... (ii) The percentage of households with this item approximately doubled between and Answer... (iii) The percentage of households with this item increased by approximately five times between and Answer... TS/Mar07/FMFTB2 Page 28

29 11 LEAVE MARGIN BLANK (c) (i) Describe how the percentage of households with mobile phones changes between and (ii) Daniel says that the percentage of households with mobile phones will double over the next five years. Explain why this is not possible (d) The table gives more information about households with telephones. Year Total number of households (nearest million) Households with a telephone % % Use the information to calculate the difference between the number of households with telephones in and ? You must show your working TS/Mar07/FMFTB2 Answer... END OF QUESTIONS Page 29 (4 marks) Turn over 10

30 12 There are no questions printed on this page DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED Copyright 2008 AQA and its licensors. All rights reserved. Page 30 APW/SPP08/93002/FA

31 abc General Certificate of Secondary Education Mathematics 9307 (Including Functional Mathematics) Specimen Mark Scheme Paper 2 Functionality Mark Scheme 2008 examination - June series Page 31

32 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 2007 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester M15 6EX Dr Michael Cresswell Director General Page 32

33 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Paper 2 Functionality Question Answer Mark Comment 1(a) 25 B1 1(b) 35 ( ) M1 Condone missing brackets or A1 1(c) ( ) 3 seen D1 Their ( ) Their ( ) 3 M1 ( ) 102 A1 SC1 for ( )105 1(d) Friday + Saturday + Sunday = 9 and Friday 5 and Saturday 5 and Sunday 2 B2 B1 for any two conditions correct 1(e) ( 6) or 105 M ( 5) or 150 M1 Ray A1 1(f) 21 ( ) 4.50 or ( ) 94.5 M1 (Overtime =) or ( ) 6.75 M1 or (Overtime =) or 6 (hours) oe Their Their M1dep Their Their or Their ( ) A1 ( ) scores M1M1M1A0 Page 33

34 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Question Answer Mark Comment 2(a) 25 to 30 D1 2(b) Healthy D1 2(c) 25 D1 2(d)(i) M (.10 ) A1 27 (.10 ) 2(d)(ii) Overweight D1ft or ft from Their answer in part (d)(i) 2(e) 67 D D1 SC1 for any value(s) from healthy range ie, 67 w 91 with no value(s) outside range 2(f) seen M1 8 or 9 A1 2(g)(i) 23 = W M1 (W=) 23 Their (W=) 23 Their 3.24 or M1 74 (.52 ) A1 Accept inclusive inclusive implies M1M1 2(g)(ii) BMI will be smaller or lower B1 Accept more healthy, more underweight, less overweight, thinner, slimmer BMI is inversely proportional to height (squared) B1 Accept convincing explanation based on formula and/or graph eg, BMI is smaller because you are dividing by a larger number scores B2 Accept an example given which justifies smaller BMI eg, 1.80! BMI ! BMI 6.37 Page 34

35 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Question Answer Mark Comment 3(a) 5 B1 3(b) 6 and 7 B1 3(c) Valid explanation B1 Accept: Must be a multiple of four Do not accept: Because even 3(d) All four correct: B3 Any two or three correct: B2 8, 1 2, 7 Any one correct: B1 6, 3 4, 5 If none correct: B1 for all four pairs seen (any order, anywhere) 3(e) 13 B1 3(f) M or counting to the middle: 8, 9, 10, 11, , 14, 15, 16, 17 or counting outwards, at least two of: 7 and 18; 6 and 19; 5 and 20; 4 and 21; 3 and 22; 2 and 23; 1 and A1 Page 35

36 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Question Answer Mark Comment 4(a) Faster in Leeds or Slower in Paris B1 4(b) 3 B1 4(c) Moderate visibility D1 oe 4(d)(i) Sunday D1 4(d)(ii) Saturday D1 4(e)(i) 4 B1 Accept 4 4(e)(ii) Saturday and Paris B1 4(e)(iii) Attempt to work out daily variation for Leeds or Paris Attempt tp work out an average value of daily variation for Leeds or Paris M1 Leeds: 3, 6, 6, 5, 3 Paris: 6, 2, 8, 7, 2 M1 Leeds Mean = 23 5 or 3, 3, 5, 6, 6 Paris Mean = 26 5 or 2, 2, 7, 7, 8 ft Their daily variations 4.6 and 5.2 or 5 and 7 A1 Allow 23 and 26 Paris A1 With correct method Page 36

37 Functional Mathematics - AQA GCSE Mark Scheme 2008 June Series Question Answer Mark Comment 5(a) 58 or 59% D1 5(b)(i) Microwave D1 5(b)(ii) Home computer D1 5(b)(iii) Internet connection D1 5(c)(i) Increases D1 5(c)(ii) Cannot double when more than 50% already D1 5(d) or M1 oe 19 or A1 or and M1 or A1 oe Page 37

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39 abc General Certificate of Secondary Education MATHEMATICS (PILOT) Unit 1 Functional Mathematics Data Book (Examination) 93001/PM Specimen Paper (Curriculum Pathways Pilot) 2008 Instructions This copy of the Data Book is for use in the examination. It should not be given to candidates in advancel. Page /PM

40 2 There is no source material printed on this page TS/Mar07/DS Page 40

41 3 Data Sheet for Holiday Jobs These tables show the regulations for summer holiday jobs for people aged 13 to 18 years. Work regulations for people aged 13 to 18 years Holiday Jobs: hours of work Age under 13 Legally not allowed to work A maximum of 25 hours per week Age 13 to 14 Up to 5 hours a day from Monday to Saturday Up to 2 hours a day on Sunday A maximum of 35 hours per week Age 15 and over Up to 8 hours a day from Monday to Saturday Up to 2 hours a day on Sunday Holiday Jobs: rates of pay Age under 16 Pay not covered by minimum wage Age 16 to 17 Minimum wage 3.00 per hour Age 18 and over Minimum wage 4.25 per hour TS/Mar07/DS Page 41

42 4 Data Sheet for Body-Mass Index (Adults) Body-Mass Index (BMI) is a way of comparing people using their height and body mass (weight). It is calculated using the formula: BMI = body mass 2 height Body mass is measured in kilograms. Height is measured in metres. The table shows the different ranges of BMI. Classification BMI range Underweight Less than 18.5 Healthy 18.5 to 25 Overweight 25 to 30 Obese Over 30 TS/Mar07/DS Page 42

43 5 Body-Mass Index (BMI) Graph for Adults underweight healthy overweight height (m) BMI = 18.5 line BMI = 25 line BMI = 30 line obese body mass (kg) TS/Mar07/DS Page 43

44 6 Data Sheet for Weather These tables show the weather forecast for 5 days in Leeds and Paris. Key: Sunny Sunny intervals Cloudy Rain Leeds Day Summary Max Day C Temperature Min Night C Wind speed (mph) Visibility Friday Good Saturday Poor Sunday Poor Monday Poor Tuesday Poor Paris Day Summary Max Day C Temperature Min Night C Wind speed (mph) Visibility Friday Moderate Saturday Moderate Sunday Good Monday Good Tuesday Moderate TS/Mar07/DS Page 44